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Abstract

Abstract. In this paper we address the problem of aligning 3-D data with articulated shapes. This problem resides at the core of many motion tracking methods with applications in human motion capture, action recognition, medical-image analysis, etc. We describe an articulated and bending surface representation well suited for this task as well as a method which aligns (or registers) such a surface to 3-D data. Articulated objects, e.g., humans and animals, are covered with clothes and skin which may be seen as textured surfaces. These surfaces are both articulated and deformable and one realistic way to model them is to assume that they bend in the neighborhood of the shape’s joints. We will introduce a surface-bending model as a function of the articulated-motion parameters. This combined articulated-motion and surface-bending model better predicts the observed phenomena in the data and therefore is well suited for surface registration. Given a set of sparse 3-D data (gathered with a stereo camera pair) and a textured, articulated, and bending surface, we describe a register-and-fit method that proceeds as follows. First, the data-to-surface registration problem is formalized as a classifier and is carried out using an EM algorithm. Second, the data-to-surface fitting problem is carried out by minimizing the distance from the registered data points to the surface over the joint variables. In order to illustrate the method we applied it to the problem of hand tracking. A hand model with 27 degrees of freedom is successfully registered and fitted to a sequence of 3-D data points gathered with a stereo camera pair. 1

Citations

...3, pp. 578–591, 2006. c○ Springer-Verlag Berlin Heidelberg 2006sThe Alignment Between 3-D Data and Articulated Shapes 579 A first class of methods addresses the problem of articulated object tracking =-=[1]-=-. A human motion tracker, for example, uses a previously estimated pose as a prior to predict the current pose and to update the model’s parameters [2], [3], [4], [5], [6]. Objects may have large moti...

.... There are two classes of techniques available for solving this problem. The first class describes the object as a point data set and estimates the motion parameters using point-to-point assignments =-=[9]-=-. This type of methods works well provided that point-assignments (that may well be viewed as hidden variables) are properly established. The second class of techniques describes the object as a param...

... algorithm able to deal with outliers [13]. However, they constrain the points to be assigned pair-wise which leads to some difficulties, as explained in section 4. The idea of using the EM algorithm =-=[14]-=- for solving the point matching problem was used by others [15], [16], [17]. However, previous work did not attempt to with articulated shapes. Moreover, the prolem of outlier rejection is not handled...

...problem of articulated object tracking [1]. A human motion tracker, for example, uses a previously estimated pose as a prior to predict the current pose and to update the model’s parameters [2], [3], =-=[4]-=-, [5], [6]. Objects may have large motion amplitudes between two video frames and their aspect may drastically change as one body part is occluded by another one or when it turns away from the camera’...

...primarily been addressed in the case of rigid and deformable objects, and has barely been considered in the case of articulated objects. The idea of approximatively matching sets of points stems from =-=[11]-=-. [12]. These same authors propose a point matching algorithm able to deal with outliers [13]. However, they constrain the points to be assigned pair-wise which leads to some difficulties, as explaine...

...sidered in the case of articulated objects. The idea of approximatively matching sets of points stems from [11]. [12]. These same authors propose a point matching algorithm able to deal with outliers =-=[13]-=-. However, they constrain the points to be assigned pair-wise which leads to some difficulties, as explained in section 4. The idea of using the EM algorithm [14] for solving the point matching proble...

... articulated object tracking [1]. A human motion tracker, for example, uses a previously estimated pose as a prior to predict the current pose and to update the model’s parameters [2], [3], [4], [5], =-=[6]-=-. Objects may have large motion amplitudes between two video frames and their aspect may drastically change as one body part is occluded by another one or when it turns away from the camera’s field of...

...ay have large motion amplitudes between two video frames and their aspect may drastically change as one body part is occluded by another one or when it turns away from the camera’s field of view [7], =-=[8]-=-. Image data are often ambiguous and it is not easy to separate the tracked object from the background or from other moving objects. A second class of methods addresses the problem of aligning (or reg...

...em of articulated object tracking [1]. A human motion tracker, for example, uses a previously estimated pose as a prior to predict the current pose and to update the model’s parameters [2], [3], [4], =-=[5]-=-, [6]. Objects may have large motion amplitudes between two video frames and their aspect may drastically change as one body part is occluded by another one or when it turns away from the camera’s fie...

...rain the points to be assigned pair-wise which leads to some difficulties, as explained in section 4. The idea of using the EM algorithm [14] for solving the point matching problem was used by others =-=[15]-=-, [16], [17]. However, previous work did not attempt to with articulated shapes. Moreover, the prolem of outlier rejection is not handled by their EM algorithms. The remainder of this paper is organiz...

...nts (that may well be viewed as hidden variables) are properly established. The second class of techniques describes the object as a parameterized surface (or a curve) and fits the latter to the data =-=[10]-=-, [2], [3]. This type of methods works well provided that the data are not too far from the object, that the data are evenly distributed around the object and that they are not corrupted by large-ampl...

...nts to be assigned pair-wise which leads to some difficulties, as explained in section 4. The idea of using the EM algorithm [14] for solving the point matching problem was used by others [15], [16], =-=[17]-=-. However, previous work did not attempt to with articulated shapes. Moreover, the prolem of outlier rejection is not handled by their EM algorithms. The remainder of this paper is organized as follow...

...ily been addressed in the case of rigid and deformable objects, and has barely been considered in the case of articulated objects. The idea of approximatively matching sets of points stems from [11]. =-=[12]-=-. These same authors propose a point matching algorithm able to deal with outliers [13]. However, they constrain the points to be assigned pair-wise which leads to some difficulties, as explained in s...

...esses the problem of articulated object tracking [1]. A human motion tracker, for example, uses a previously estimated pose as a prior to predict the current pose and to update the model’s parameters =-=[2]-=-, [3], [4], [5], [6]. Objects may have large motion amplitudes between two video frames and their aspect may drastically change as one body part is occluded by another one or when it turns away from t...

... the problem of articulated object tracking [1]. A human motion tracker, for example, uses a previously estimated pose as a prior to predict the current pose and to update the model’s parameters [2], =-=[3]-=-, [4], [5], [6]. Objects may have large motion amplitudes between two video frames and their aspect may drastically change as one body part is occluded by another one or when it turns away from the ca...

...cts may have large motion amplitudes between two video frames and their aspect may drastically change as one body part is occluded by another one or when it turns away from the camera’s field of view =-=[7]-=-, [8]. Image data are often ambiguous and it is not easy to separate the tracked object from the background or from other moving objects. A second class of methods addresses the problem of aligning (o...

...he points to be assigned pair-wise which leads to some difficulties, as explained in section 4. The idea of using the EM algorithm [14] for solving the point matching problem was used by others [15], =-=[16]-=-, [17]. However, previous work did not attempt to with articulated shapes. Moreover, the prolem of outlier rejection is not handled by their EM algorithms. The remainder of this paper is organized as ...